Singular Perturbation Techniques Applied to Multiasset Option Pricing

30 Pages Posted: 30 Jun 2009

See all articles by Peter Duck

Peter Duck

University of Manchester - Department of Mathematics

Chao Yang

University of Manchester

David Newton

University of Bath - School of Management

Martin Widdicks

Lancaster University - Department of Accounting and Finance

Date Written: 2007-10

Abstract

It is well known that option valuation problems with multiple-state variables are often problematic to solve. When valuing options using lattice-type techniques such as finite-difference methods, the curse of dimensionality ensures that additional-state variables lead to exponential increases in computational effort. Monte Carlo methods are immune from this curse but, despite advances, require a great deal of adaptation to treat early exercise features. Here the multiunderlying asset Black–Scholes problem, including early exercise, is studied using the tools of singular perturbation analysis. This considerably simplifies the pricing problem by decomposing the multi-dimensional problem into a series of lower-dimensional problems that are far simpler and faster to solve than the full, high-dimensional problem. This paper explains how to apply these singular perturbation techniques and explores the significant efficiency improvement from such an approach.

Suggested Citation

Duck, Peter and Yang, Chao and Newton, David and Widdicks, Martin, Singular Perturbation Techniques Applied to Multiasset Option Pricing (2007-10). Mathematical Finance, Vol. 19, Issue 3, pp. 457-486, July 2009, Available at SSRN: https://ssrn.com/abstract=1426630 or http://dx.doi.org/10.1111/j.1467-9965.2009.00373.x

Peter Duck (Contact Author)

University of Manchester - Department of Mathematics ( email )

Oxford Road
Manchester M60 1QD, N/A M13 9PL
United Kingdom

Chao Yang

University of Manchester

Oxford Road
Manchester, N/A M13 9PL
United Kingdom

David Newton

University of Bath - School of Management ( email )

Claverton Down
Bath, BA2 7AY
United Kingdom

Martin Widdicks

Lancaster University - Department of Accounting and Finance ( email )

Lancaster, Lancashire LA1 4YX
United Kingdom

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